Modelling &Simulation of a Three-Phase Electric Traction Induction ... · PDF fileFigure1The...

International Journal of Electrical, Electronics and Computer Systems (IJEECS)

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ISSN (Online): 2347-2820, Volume -2, Issue-5, 6, 2014

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Modelling &Simulation of a Three-Phase Electric Traction Induction

Motor Using Matlab Simulink

1Naveed Rahaman,

2H.V. Govindraju

M-tech Student1, Associate Professor

2, Dept. of EEE,

Dr. AIT, Bangalore, Karnataka, India

Email: [email protected];

[email protected];

Abstract– The theory of reference frames has been

effectively used as an efficient approach to analyze the

performance of the induction electrical machines. This

paper presents a step by step Simulink implementation of

an induction machine using dq0 axis transformations of the

stator and rotor variables in the arbitrary reference frame.

For this purpose, the relevant equations are stated at the

beginning, and then a generalized model of a three phase

induction motor is developed and implemented in an easy

to follow way. The obtained simulated results provide clear

evidence that the reference frame theory is indeed an

attractive algorithm to demonstrate the steady-state

behavior of the induction machines. The designed induction

motor model is then given the input supply from an IGBT 2

level inverter controlled by space vector PWM. The speed

control of the designed traction induction motor is achieved

by PI controller based on closed loop voltage control.

Keywords: Induction motor, D-Q transformation, Electric

traction, Flux linkage, Speed, Torque, SVPWM, Inverter.

A. INDUCTION MOTOR MODELLING

I. INTRODUCTION

The voltage and torque equations that describe the

dynamic behaviour of an induction motor are time-

varying. It is successfully used to solve such differential

equations and it may involve some complexity. A

change of variables can be used to reduce the

complexity of these equations by eliminating all

time-varying inductances, due to electric circuits in

relative motion, from the voltage equations of the

machine[1,2,3,4]. By this approach, a poly phase

winding can be reduced to a set of two phase windings

(q-d)with their magnetic axes formed in quad rature. In

other words, the stator and rotor variables (voltages,

currents and flux linkages) of an induction machine are

transferred to a reference frame, which may rotate at any

angular velocity or remain stationary. Such a frame of

reference is commonly known in the generalized

machines analysis as arbitrary reference frame[5,6, 7].

Figure1The dq0 equivalent circuit of an induction motor

The dynamic analysis of the symmetrical induction

machines in the arbitrary reference frame has been

intensively used as a standard simulation approach from

which any particular mode of operation may then be

developed.

Matlab/ Simulink has an advantage over other machine

simulators in modelling the induction machine using

dq0 axis transformation [8,9]. It can be a powerful

techniqueinimplementingthemachineequationsastheyaret

ransferredto a particular reference frame. Thus, every

single equation among the model equations can be easily

implemented in one block so that all the machine

variables can be made available for control and

verification purposes. In this paper, Matlab/Simulink is

used to simulate the dynamic performance of an

induction motor model whose stator and rotor variables

are referred to an arbitrary reference frame [1, 6, 8, 10].

The provided machine model is simulated in a way that

makes it easy for the reader to follow and understand the

implementation process since it gives full details about

Simulink structure of each of the model equations. The

equivalent circuit of the induction machine in the

arbitrary reference frame is shown in figure 1 below [11,

12].

II. INDUCTION MOTOR MODEL

Driving the model equations can be generated from the

dq0 equivalent circuit of the induction machine shown

in figure 1. The flux linkages equations associated with

this circuit can be found as follows:

mailto:[email protected]

mailto:[email protected]


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dλqs

dt= ωb Vqs −

ωe

ωbλds +

Rs

Xls λmq − λqs . . . . . . .(1)

dλds

dt= ωb Vds −

ωe

ωbλqs +

Rs

Xls λmd − λds . . . . . . .(2)

dλqr

dt= ωb Vqr −

ωe−ωr

ωbλdr +

Rr

Xlr λmq − λqr . . .(3)

dλdr

dt= ωb Vdr −

ωe−ωr

ωbλqr +

Rr

Xlr λmq − λdr . . .(4)

Where

λmq = Xml λqs

Xls+

λqr

Xlr . . . . .. . . . .. . . . .. . . . . .(5)

λmd = Xml λds

Xls+

λdr

Xlr . . . . . . . . . . . . . . . . . . . . .(6)

Xml =1

1

Xm+

1

Xls+

1

Xlr . .. . . . .. . . . .. . . . . . . . . . . . (7)

Then substituting the values of the flux linkages to find

the currents;

Iqs =1

Xls λqs − λmq . . . . . . . . . . . . . . . . . . . . . . . . .(8)

Ids =1

Xls λds − λmd . .. . . . .. . . . .. . . . . . . . . . . . .(9)

Iqr =1

Xlr λqr − λmq . . . . . . . . . . . . . . . . . . . . . . . . (10)

Idr =1

Xlr λdr − λmd . .. . . . .. . . . .. . . . . . . . . . . . (11)

Based on the above equations, the torque and rotor

speed can be determined as follows:

Te =3

2

P

2

1

ωb λdsIqs + λqsIds . . .. . . . .. . . . . . . .(12)

ωr = P

2J Te− Tl . . .. . . . .. . . . . . . . . . . . . . . . . . (13)

Where P: number of poles; J: moment of inertia (Kg/m2)

For squirrel cage induction motor, the rotor voltages Vqr

and Vdr in the flux equations are set to zero since the

rotor cage bars are shorted. After driving the torque and

speed equations in term of d-q flux linkages and current

soft he stator, the d-q axis transformation should now be

applied to the machine input(stator)voltages[1,13,14].

The three-phase stator voltages of an induction machine

under balanced conditions can be expressed as:

Va = √2 Vrms sin(ωt). . . . .. . . . . . . . . . . . . . . . . . (14)

Vb = √2 Vrms sin(ωt −2π

3). . . . .. . . . . . . . . . . . . .(15)

Vc = √2 Vrms sin(ωt +2π

3). . . . ... . . . . . . . . . . . . (16)

These three-phase voltages are transferred to a

synchronously rotating reference frame in only two

phases (d-q axis transformation). This can be done using

the following two equations.

Vα

Vβ =

2

3 1 −1

2 −1

2

0 √32

−√32

VaVbVc

... . . . . . .. . . . . (17)

Then, the direct and quadrature axes voltages are

VdVq

= cosθ sinθ

−sinθ cosθ

Vα

Vβ ... . . . . . . . . . .. . . . . . . (18)

The instant aneous values of the stator and rotor currents

in three-phase system are ultimately calculated using the

following transformation:

IαIβ

= cosθ −sinθ

sinθ cosθ

IdIq

... . . . . . . . . . . . . . . . . . . (19)

IaIbIc

=2

3

1 0

−12

√32

−12

−√32

... . . . . . . . . .. . . . . . . . . . (20)

III MATLAB/SIMULINK

IMPLEMENTATION

In this section, the three phase induction machine model

is simulated by using the Matlab/Simulink. The Model is

implemented using the same set of equations provided

above in sections II. Figure 2 depicts the complete

Simulink scheme of the described induction machine

model.

Figure 2 the 3-phase induction motor Matlab/Simulink

model

In this model the simulation starts with generating a

three-phase stator voltages according to the equations

(14, 15, 16), and then transforming these balanced

voltages to two phase voltages referred to the


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synchronously rotating frame using Clarke and Park

transformation as in equations (17, 18). After that the d-

q flux linkage and current equations were implemented

as to be demonstrated below. Figure 3 illustrates the

internal structure of the induction machine d-q model by

which the flux linkages, currents, torque and the rotor

angular speed are calculated.

Figure 3 the internal structure of the 3-phase induction

motor d-q model

The Matlab/Simulink model to find the Flux linkage λqs,

λqr, λds, λdr, as stated in equations (1)-(4) is shown in

figure 4.

Figure 4 the internal structure of the block to calculate

the flux linkages

Figures.5 show the Simulink blocks used to calculate the

currents Iqs, Ids, Iqr,Idr, according to the equations (8) –

(11), also λmq, λmd in equations (5), (6). Figures 6 show

the implementation of torque Te and angular speed ωr as

expressed in equations (12), (13) respectively.

Figure 5 the internal structure of the block to calculate

the currents Iqs, Ids, Iqr,Idr, and the fluxes λmq, λmd.

Figure. 6 the implementation of the torque equation Te

(12) and the angular speed equation ωr (13)

Figure.7 shows the internal structure of the blocks (1- 4)

in figure 4 in which the equations (1)-(4) are

implemented in Matlab/Simulink format.

Figure 7 the implementation of the equation (1)-(4)

IV. MATLAB/SIMULINK RESULTS

The simulation results are given for the induction motor

with the following specifications:


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KW = 285, VL = 1140, P = 4, f = 50, Rs = 0.131, Xls =

0.589,Rr = 0.0905, Xlr = 0.589, J = 4, Xm = 19.11, rpm

= 3000

Figure8 Torque speed characteristics for given induction

motor

Figure9Machine variables during free acceleration of

induction motor

Figure10Torque & speed characteristics of induction

motor

Finally, the machine parameters should be defined to the

simulated machine system in order to complete the

simulation process. There are many ways to input the

required data. The method used here is the graphical

user interface (GUI). The machine parameters are

entered through the convenient graphical user interface

(GUI) available in Matlab/Simulink, where you can


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right click with your mouse and then choose parameters

to be added (edit mask). Figure 11 shows the GUI of the

induction machine d-q model shown earlier in figure 2.

After achieving the Matlab/Simulink implementation of

the described machine model using the

Matlab/Simulink, a Matlab code program was assigned

to the same model using the same set of equations. The

code provided similar results to those obtained by

Matlab/Simulink. However, it was found that

Matlab/Simulink is more convenient in terms of

simplicity in construction and control algorithms which

may be set forth for this model. The code compilation

steps can be stated by the flow chart shown below in

figure 11.

Figure 11 the graphical user interface (GUI) used to

define the input data to the simulated induction motor.

V. INDUCTION MOTOR WITH INVERTER

CLOSED LOOP VOLTAGE CONTROL

In this section, the three phase induction machine model

with inverter and closed loop voltage control system is

simulated by using the Matlab/Simulink. Here the

actual speed of the induction motor is compared with the

reference speed; the difference between them is error.

The error signal fed to the PI controller and then

controlled output is then given as reference to the

controlled dc voltage source for the inverter input.

Figure 12 depicts the complete Simulink scheme of the

described model. Figures 13 show the 3 phase - 2 level

IGBT based inverter. It also provided with the 2nd

order

low pass filter to get pure sine wave output from the

inverter.

Figure 12: Simulink model of PI controller based three

phase Induction motor voltage control

Figure 13: Internal structure of the 3-phase igbt based

inverter model

VI. MATLAB/SIMULINK RESULTS

The simulation results are given for the induction motor

with the closed loop control system at different

reference speed and load torque:

1. Reference speed NS = 1500 and Load Torque

TL=1000:

Figure 14: Torque speed characteristics for given

induction motor at NS=1500 & TL=1000


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Figure 15: Torque & speed characteristics of induction

motor at NS=1500 & TL=1000

Figure 16: Machine current during closed loop at

NS=1500 & TL=1000

Figure 17: Inverter output voltages during closed loop at

NS=1500 & TL=1000

The figures 18 and the figure 19 show the frequency

spectrum of the phase voltage and the line voltage after

2nd

order low pass filter. The value of the THD for phase

voltage is 54.12% while for the line voltage it is 10.88%.

The value of the fundamental component of the phase

voltage is 548.2 V while for the line it is 948.4 V for the

dc input voltage of 1140 V.

Figure 18: THD in phase voltage Va at NS=1500 &

TL=1000

Figure 19: THD in LP filter output phase voltage Va at

NS=1500 & TL=1000

2. Reference speed NS = 1500 and Load Torque

TL=2035:

Figure 20: Torque speed characteristics for given

induction motor at NS=1500 & TL=2035


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Figure 21: Torque & speed characteristics of induction

motor at NS=1500 & TL=2035

Figure 22: Machine current during closed loop at

NS=1500 & TL=2035

Figure 23: Inverter output voltages during closed loop at

NS=1500 & TL=2035

Figure 24: THD in phase voltage Va at NS=1500 &

TL=2035

Figure 25: THD in LP filter output phase voltage Va at

NS=1500 & TL=2035

The figures 24 and the figure 25 show the frequency

spectrum of the phase voltage and the line voltage after

2nd

order low pass filter. The value of the THD for phase

voltage is 53.03% while for the line voltage it is 6.80%.

The value of the fundamental component of the phase

voltage is 768.8 V while for the line it is 1330 V for the

dc input voltage of 1140 V.

VII. CONCLUSIONS

In this paper, an implementation and dynamic modeling

of a three-phase induction motor using Matlab/Simulink

are presented in a step-by-step manner and its speed

control is achieved using voltage control by closed loop

PI control system. The parameters are obtained from the

testing done on the electrical traction induction motor.

The model was tested at three different load torque of a

small and large induction motors. The simulated

machine has given a satisfactory response in terms of the

torque and speed characteristics. Also, the model was

controlled from an IGBT based 2 level inverter at

different load torque conditions. Both physical and

simulation methods have given almost same results for

the three phase induction motors used for traction

purpose. There is appreciable improvement in THD in

inverter line and phase voltage as the modulation index

is increased and close to unity. From the analysis we


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conclude that as the modulation index increased. This

concludes that the Matlab/Simulink is a reliable and

sophisticated way to analyse and predict the behaviour

of induction motors using the theory of reference

frames. Total harmonic distortion THD in line and phase

voltage decreases as the value of load torque increased.

The value of fundamental component in line and phase

voltage is increased with the increase in load torque.

REFERENCES

[1] P. C. Krause, O. Wasynczuk, S. D. Sudhoff

“Analysis of Electric Machinery and Drive

Systems”, IEEE Press, A John Wiley & Sons,

Inc. Publication Second Edition, 2002.

[2] M. L. de Aguiar, M. M. Cad, “The concept of

complex transfer functions applied to the

modeling of induction motors”, Power

Engineering Society Winter Meeting, 2000, pp.

387–391.

[3] S. Wade, M. W. Dunnigan, B. W. Williams,

“Modeling and simulation of induction machine

vector control with rotor resistance

identification”, IEEE Transactions on Power

Electronics, vol. 12, No. 3, May 1997, pp. 495–

506.

[4] B. Ozpineci, L. M. Tolbert, “Simulink

implementation of induction machine model – A

Modular approach”, Ieee, 2003, pp 728-734.

[5] H. C. Stanley, “An Analysis of the Induction

Motor”, AIEE Transactions, Vol.

57(Supplement), 1938, pp. 751-755.

[6] H. C. Stanley, “An Analysis of the Induction

Motor”, AIEE Transactions, Vol. 57

(Supplement), 1938, pp. 751-755.

[7] G. McPherson and R. D. Laramore, “an

Introduction to Electrical Machines and

Transformers”, 2rd ed., John Wiley and Sons,

New York, 1990.

[8] J. O. P. Pinto, B. K. Bose, L. E. B. Silva, M. P.

Kazmierkowski, “A neural-network-based

space-vector PWM controller for voltage-fed

inverter induction motor drive,” IEEE

Transactions on Industry Applications, vol. 36,

no. 6, Nov./Dec. 2000, pp. 1628–1636.

[9] Bose B.K., Power Electronics and AC Drives,

Englewood Cliffs, NJ: Prentice Hall, 1986

[10]. Frede Blaabjerg,, Sigurdur Freysson, Hans-

Henrik Hansen, and S. Hansen “A New

Optimized Space-Vector Modulation Strategy for

a Component-Minimized Voltage Source Inverter

” IEEE Trans. on Power Electronics, Vol. 12, No.

4, July 1997, pp 704-710.

[11] Scott Wade, Matthew W. Dunnigan, and Barry

W. Williams, “Modelling and Simulation of

Induction Machine Vector Control with Rotor

Resistance Identification”, IEEE transactions on

power electronics, vol. 12, no. 3, may 1997.

[12] Ramon Blasco Blasco Gimenez, “High

Performance Sensorless Vector Control of

Induction Motor Drives”, The University of

Nottingham, December 1995

[13] Adel Aktaibi, Daw Ghanim, and M. A. Rahman,

“Dynamic Simulation of a Three-Phase Induction

Motor using Matlab Simulink”.

[14] S. Senthilkumar and S. Vijayan, “Simulation of

High Performance PID Controller for Induction

Motor Speed Control with Mathematical

Modelling”, Research Journal of Applied

Sciences, Engineering and Technology 6(18):

3343-3348, 2013. ISSN: 2040-7459.

[15] Amit Kumar Sharma, Tushar Deep Saxena,

Shirazul Islam, Arunkumar Yadav, “Performance

Analysis of Three Phase PWM Voltage Source

Inverter Fed Three Phase Induction Motor

Drive”, IJAEEE, ISSN : 2278-8948, Volume-2,

Issue-2, 2013.

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